the average age of class having 35 students is 14 years when the age of the class teacher is added to the sum of the age of students the average Rises by 0.5 year. what must be the age of teacher ?

Dear Student
35  = n
14 = average i.e. mean
summation of X = average x n
= 14 x 35
= 490

given : average rises by 0.5 yrs when teacher's age is added
therefore, average = 14.5
Assume age of teacher be x
(490 + x) / (35 + 1) = 14.5
(35+1) because teacher's age is included
 (490 + x) = (14.5 x 36)
x = 522 - 490
x = 32 yrs

Age of teacher will be 32 years
regards